In [1]} we prove for \(H_2(x,-1)\) , defined as the limit of \(H_2(x,y)\)  for
\(y \downarrow -1\) , the following property
\(H_2(a_0,b_1,b_2,c_1,c_2;x,-1)&=\dfrac{\Gamma (1-a_0)\Gamma (1-a_0-b_2-c_1)}{\Gamma (1-a_0-b_2)\Gamma (1-a_0-c_1)}\,\mbox{}_{3}F_{2}\!\left(\genfrac{}{}{0.0pt}{}{a_0+b_2,a_0+c_1,b_1}{a_0+b_2+c_1,c_2};x\right)+ \\&+\dfrac{\Gamma (1-a_0)\Gamma (a_0+b_2+c_1-1)}{\Gamma (b_2)\Gamma (c_1)}\dfrac{\Gamma (c_2)\Gamma (b_1-a_0-b_2-c_1+1)}{\Gamma (b_1)\Gamma (c_2-a_0-b_2-c_1+1)} \\&\qquad \qquad x^{1-a_0-b_2-c_1}\,\mbox{}_{3}F_{2}\!\left(\genfrac{}{}{0.0pt}{}{1-b_2,1-c_1,b_1-a_0-b_2-c_1+1}{2-a_0-b_2-c_1,c_2-a_0-b_2-c_1+1};x\right)\) 
